Statistics E Commerce

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Statistics help ASAP please!?

A local chamber of commerce is backing a plan for a new convention center. The chamber states that 65 percent of the voters favor the plan, which would raise tourism business and taxes for the residents. 5 of the registered voters in the community are called at random. X is the number of voters called who say they favor the plan. Find the probability that exactly 2 voters sampled favor the plan. Round to 6 decimal places with zero in the units place (i.e. 0.xxxxxx)

Let X be the number of voters who favor the plan. X has the binomial distribution with n = 5 trials and success probability p = 0.65

In general, if X has the binomial distribution with n trials and a success probability of p then
P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P[X = x] = 0 for any other value of x.

The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.
Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.

X ~ Binomial( n = 5 , p = 0.65 )

the mean of the binomial distribution is n * p = 3.25
the variance of the binomial distribution is n * p * (1 - p) = 1.1375
the standard deviation is the square root of the variance = √ ( n * p * (1 - p)) = 1.066536

The Probability Mass Function, PMF,
f(X) = P(X = x) is:

P( X = 0 ) = 0.005252187
P( X = 1 ) = 0.04877031
P( X = 2 ) = 0.1811469 <<<< ANSWER
P( X = 3 ) = 0.3364156
P( X = 4 ) = 0.3123859
P( X = 5 ) = 0.1160291

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